Working on my Nintendo Kirby alternate universe where things are more biologically realistic.
Many life forms are roundish legless creatures that can move by bouncing. How can this work and is it as efficient as legs?
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Give them a hydrostatic skeleton.
Earthworms are roundish, legless creatures. They don't happen to move by bouncing, but they get along quite well without any bones or joints. How?
They have cavities inside their bodies that are filled with incompressible fluid, and muscles wrapped around those cavities in different directions. Flex one set of muscles, and because the fluid is not compressible, the cavity is forced to elongate. Flex a different set of muscles, running perpendicular to the first set, and the cavity contracts.
In the case of movement by bouncing, you'd need the muscles be fast enough and strong enough that the mere inertia of the fluid in the cavity when it's being elongated (presumably "upwards", perpendicular to the ground) is enough to lift the creature off the ground for a moment. But the concept is there.
(Can this be as efficient as legs? That's above my pay grade, I'm afraid--although the apparent lack of existing organisms that travel by bouncing might leave a clue...)
First of all, They would need some way of initiating motion. At the very least, they might need a scaly sort of skin such as snakes use to start moving. OK, now they are rolling. If they are flexible, then they could move some muscles to effectively "jump" by pushing off from the current contact area. Then, as comments suggest, a series of jumps as kangaroos and various rodents use would be fast if not energy-efficient.